Jolie, who oddly never picks up a gun, is joined in boring chases through the canals and over the rooftops by Johnny Depp — with whom she has no romantic chemistry whatsoever, no matter how many passionless kisses they share.

The basic setup is that Jolie’s character, Elise — a mystery lady with an instantly guessed secret — has been contacted in Paris by an ex-lover who’s stolen zillions of dollars and changed his appearance through plastic surgery to elude detection.

The ex-lover sends a note asking Elise to take a train to Venice — and along the way, to pick up a stranger of his size and build so the authorities will think it’s him.

Because Elise is played by Angelina Jolie with Madonna’s old British accent, she has no problem acquiring a doppelganger in Depp’s Frank. He’s identified as a widowed American math professor. Let’s just say Depp is more believable as Capt. Jack Sparrow or Willie Wonka.

Depp has an even harder time convincing us that Frank would not only continue to hang around, but volunteer to protect Elise, whom he barely knows, after bullets shatter the door of the suite in the five-star hotel that they chastely share.

Even their pursuers — teams led by a mobster (Steven Berkoff) and a Scotland Yard big shot (Paul Bettany) — aren’t terribly colorful in a movie where action scenes are few and far between.

You would think that three Oscar winners would be able to come up with a single memorable line between them. Saying that Jolie’s character “tends to fall in love with anyone she’s spent more than a train ride with” isn’t exactly a “North by Northwest”-grade quip.

Von Donnersmarck, who brilliantly depicted government surveillance in East Berlin before the fall of the wall in his earlier German film, astonishingly can’t even find a way to make Interpol’s spying interesting here.

And he utterly fails to avoid telegraphing the big twist ending halfway through the film.

The director and his veteran cinematographer, John Seale, do offer plenty of nice shots of Venice — though in all truth, Jolie is the main scenic attraction.

“The Tourist” sums itself up in a single line of dialogue: “Who would have thought your tastes were so provincial?”